The following table shows the probability of
forming a bingo, black out, or four corners within a specified
number of calls. For example the probability of a single player
forming a bingo within 25 calls is 0.06396106, or about 6.4%.

Probabilities in Bingo

Number
of Calls

Bingo

Black Out

Four Corners

X

1

0.00000000

0.00000000

0.00000000

0.00000000

2

0.00000000

0.00000000

0.00000000

0.00000000

3

0.00000000

0.00000000

0.00000000

0.00000000

4

0.00000329

0.00000000

0.00000082

0.00000000

5

0.00001692

0.00000000

0.00000411

0.00000000

6

0.00005215

0.00000000

0.00001234

0.00000000

7

0.00012492

0.00000000

0.00002880

0.00000000

8

0.00025632

0.00000000

0.00005759

0.00000000

9

0.00047305

0.00000000

0.00010367

0.00000000

10

0.00080783

0.00000000

0.00017278

0.00000000

11

0.00129986

0.00000000

0.00027150

0.00000001

12

0.00199521

0.00000000

0.00040726

0.00000003

13

0.00294715

0.00000000

0.00058826

0.00000008

14

0.00421648

0.00000000

0.00082356

0.00000018

15

0.00587167

0.00000000

0.00112304

0.00000038

16

0.00798905

0.00000000

0.00149739

0.00000076

17

0.01065272

0.00000000

0.00195812

0.00000144

18

0.01395440

0.00000000

0.00251759

0.00000259

19

0.01799309

0.00000000

0.00318894

0.00000448

20

0.02287445

0.00000000

0.00398618

0.00000747

21

0.02871003

0.00000000

0.00492410

0.00001206

22

0.03561614

0.00000000

0.00601835

0.00001895

23

0.04371249

0.00000000

0.00728537

0.00002906

24

0.05312045

0.00000000

0.00874244

0.00004359

25

0.06396106

0.00000000

0.01040767

0.00006411

26

0.07635261

0.00000000

0.01229997

0.00009260

27

0.09040799

0.00000000

0.01443910

0.00013159

28

0.10623163

0.00000000

0.01684561

0.00018423

29

0.12391628

0.00000000

0.01954091

0.00025441

30

0.14353947

0.00000000

0.02254720

0.00034692

31

0.16515993

0.00000000

0.02588753

0.00046759

32

0.18881391

0.00000000

0.02958575

0.00062345

33

0.21451154

0.00000000

0.03366654

0.00082296

34

0.24223348

0.00000000

0.03815542

0.00107617

35

0.27192783

0.00000000

0.04307870

0.00139504

36

0.30350759

0.00000000

0.04846353

0.00179362

37

0.33684876

0.00000000

0.05433790

0.00228842

38

0.37178933

0.00000000

0.06073059

0.00289866

39

0.40812916

0.00000000

0.06767123

0.00364670

40

0.44563111

0.00000000

0.07519026

0.00455838

41

0.48402328

0.00000001

0.08331894

0.00566344

42

0.52300269

0.00000001

0.09208935

0.00699602

43

0.56224021

0.00000003

0.10153441

0.00859511

44

0.60138685

0.00000007

0.11168785

0.01050513

45

0.64008123

0.00000015

0.12258423

0.01277651

46

0.67795818

0.00000031

0.13425892

0.01546630

47

0.71465810

0.00000063

0.14674812

0.01863888

48

0.74983686

0.00000125

0.16008886

0.02236665

49

0.78317588

0.00000245

0.17431898

0.02673088

50

0.81439191

0.00000472

0.18947715

0.03182247

51

0.84324614

0.00000891

0.20560286

0.03774293

52

0.86955207

0.00001654

0.22273644

0.04460528

53

0.89318170

0.00003023

0.24091900

0.05253511

54

0.91406974

0.00005441

0.26019252

0.06167165

55

0.93221528

0.00009654

0.28059978

0.07216896

56

0.94768080

0.00016894

0.30218438

0.08419712

57

0.96058846

0.00029180

0.32499074

0.09794358

58

0.97111353

0.00049778

0.34906413

0.11361456

59

0.97947539

0.00083912

0.37445061

0.13143645

60

0.98592639

0.00139853

0.40119709

0.15165744

61

0.99073928

0.00230569

0.42935127

0.17454913

62

0.99419379

0.00376192

0.45896170

0.20040826

63

0.99656346

0.00607694

0.49007775

0.22955855

64

0.99810354

0.00972311

0.52274960

0.26235263

65

0.99904080

0.01541468

0.55702826

0.29917406

66

0.99956626

0.02422308

0.59296557

0.34043944

67

0.99983122

0.03774293

0.63061418

0.38660072

68

0.99994699

0.05832999

0.67002756

0.43814749

69

0.99998812

0.08943931

0.71126003

0.49560945

70

0.99999861

0.13610330

0.75436670

0.55955906

71

1.00000000

0.20560286

0.79940351

0.63061418

72

1.00000000

0.30840429

0.84642725

0.70944095

73

1.00000000

0.45945946

0.89549550

0.79675676

74

1.00000000

0.68000000

0.94666667

0.89333333

75

1.00000000

1.00000000

1.00000000

1.00000000

Dice Probability Basics
The Probabilities of Two Dice Totals

Before you play any dice game it is good to
know the probability of any given total to be thrown. First lets
look at the possibilities of the total of two dice. The table
below shows the six possibilities for die 1 along the left
column and the six possibilities for die 2 along the top column.
The body of the table shows the sum of die 1 and die 2.

Two dice totals

Die 1

Die 2

1

2

3

4

5

6

1

2

3

4

5

6

7

2

3

4

5

6

7

8

3

4

5

6

7

8

9

4

5

6

7

8

9

10

5

6

7

8

9

10

11

6

7

8

9

10

11

12

The colors of the body of the table
illustrate the number of ways to throw each total. The
probability of throwing any given total is the number of ways
to throw that total divided by the total number of
combinations (36). In the following table the specific number
of ways to throw each total and the probability of throwing
that total is shown.

Total

Number of combinations

Probability

2

1

2.78%

3

2

5.56%

4

3

8.33%

5

4

11.11%

6

5

13.89%

7

6

16.67%

8

5

13.89%

9

4

11.11%

10

3

8.33%

11

2

5.56%

12

1

2.78%

Total

36

100%

The following shows the probability of
throwing each total in a chart format. As the chart shows the
closer the total is to 7 the greater is the probability of it
being thrown.

The Field Bet Example

Now that we understand the probability of throwing each total we
can apply this information to the dice games in the casinos to
calculate the house edge. For example consider the field bet in
craps. This bet pays 1:1 (even money) if the next throw is a 3,
4, 9, 10, or 11, 2:1 (double the bet) on the 2, and 3:1 (triple
the bet) on the 12. Note that there are 7 totals that win and
only 4 that lose which might cause someone who didn't know
better to think it was a good gamble. The player's return can be
defined as the sum of the products of the probability of each
event and the net return of that event. The following table
shows each possible total, the net return, the probability of
throwing that total, and the average return. The average return
is the product of the net return and the probability. The
player's return is the sum of the average returns.

Total

Net return

Probability

Average return

2

2

0.0278

0.0556

3

1

0.0556

0.0556

4

1

0.0833

0.0833

5

-1

0.1111

-0.1111

6

-1

0.1389

-0.1389

7

-1

0.1667

-0.1667

8

-1

0.1389

-0.1389

9

1

0.1111

0.1111

10

1

0.0833

0.0833

11

1

0.0556

0.0556

12

3

0.0278

0.0834

Total

1

-0.0278

The last row shows the player's return to
be -.0278, in other words for every $1 bet the player can
expect to lose 2.78 cents. The player's loss is the house's
gain so the house edge is the product of -1 and the player's
return, in this case 0.0278 or 2.78%.

Remember, you can beat the odds, but you can't beat the percentages.
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